John is trying to determine the height of a tree that is in his yard. He notices that if he stands 12 feet from the tree, the tip of his shadow and the tip of the shadow of the tree are at the same place. Jon is 6 feet tall and his shadow at that time of day is 8 feet long.

Part A. How long is the shadow of the tree at that time of day?

Part B. Using the given information and your answer to Part A, determine the height of the tree. Show your work.

Part C. Explain the geometric properties that allowed you to determine the answer for Part B

Question

John is trying to determine the height of a tree that is in his yard. He notices that if he stands 12 feet from the tree, the tip of his shadow and the tip of the shadow of the tree are at the same place. Jon is 6 feet tall and his shadow at that time of day is 8 feet long. 

Part A. How long is the shadow of the tree at that time of day? 

Part B. Using the given information and your answer to Part A, determine the height of the tree. Show your work. 

Part C. Explain the geometric properties that allowed you to determine the answer for Part B

amistre64 · Answer

use similar triangle ratios

amistre64 · Answer

j/s1 = t/s2

s2 = 12+s1 in this case

radar · Answer

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John is 6 ft and cast an 8 ft shadow.  The tree shadow is 12 + 8 = 20 feet as john (6 ft) is standing 12 from the tree.